Provides support for big integer calculations.
Not intended to be used by other modules (except Math::BigInt::Cached).
Other modules which sport the same functions can also be used to support Math::Bigint,
like Math::BigInt::Pari.

In order to allow for multiple big integer libraries,
Math::BigInt was rewritten to use library modules for core math routines.
Any module which follows the same API as this can be used instead by using the following:

use Math::BigInt lib => 'libname';

'libname' is either the long name ('Math::BigInt::Pari'), or only the short version like 'Pari'.

The following functions MUST be defined in order to support the use by Math::BigInt:

_new(string) return ref to new object from ref to decimal string
_zero() return a new object with value 0
_one() return a new object with value 1
_str(obj) return ref to a string representing the object
_num(obj) returns a Perl integer/floating point number
NOTE: because of Perl numeric notation defaults,
the _num'ified obj may lose accuracy due to
machine-dependend floating point size limitations
_add(obj,obj) Simple addition of two objects
_mul(obj,obj) Multiplication of two objects
_div(obj,obj) Division of the 1st object by the 2nd
In list context, returns (result,remainder).
NOTE: this is integer math, so no
fractional part will be returned.
_sub(obj,obj) Simple subtraction of 1 object from another
a third, optional parameter indicates that the params
are swapped. In this case, the first param needs to
be preserved, while you can destroy the second.
sub (x,y,1) => return x - y and keep x intact!
_dec(obj) decrement object by one (input is garant. to be > 0)
_inc(obj) increment object by one
_acmp(obj,obj) <=> operator for objects (return -1, 0 or 1)
_len(obj) returns count of the decimal digits of the object
_digit(obj,n) returns the n'th decimal digit of object
_is_one(obj) return true if argument is +1
_is_zero(obj) return true if argument is 0
_is_even(obj) return true if argument is even (0,2,4,6..)
_is_odd(obj) return true if argument is odd (1,3,5,7..)
_copy return a ref to a true copy of the object
_check(obj) check whether internal representation is still intact
return 0 for ok, otherwise error message as string

The following functions are optional, and can be defined if the underlying lib has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence slow) fallback routines to emulate these:

_from_hex(str) return ref to new object from ref to hexadecimal string
_from_bin(str) return ref to new object from ref to binary string
_as_hex(str) return ref to scalar string containing the value as
unsigned hex string, with the '0x' prepended.
Leading zeros must be stripped.
_as_bin(str) Like as_hex, only as binary string containing only
zeros and ones. Leading zeros must be stripped and a
'0b' must be prepended.
_rsft(obj,N,B) shift object in base B by N 'digits' right
For unsupported bases B, return undef to signal failure
_lsft(obj,N,B) shift object in base B by N 'digits' left
For unsupported bases B, return undef to signal failure
_xor(obj1,obj2) XOR (bit-wise) object 1 with object 2
Note: XOR, AND and OR pad with zeros if size mismatches
_and(obj1,obj2) AND (bit-wise) object 1 with object 2
_or(obj1,obj2) OR (bit-wise) object 1 with object 2
_mod(obj,obj) Return remainder of div of the 1st by the 2nd object
_sqrt(obj) return the square root of object (truncate to int)
_fac(obj) return factorial of object 1 (1*2*3*4..)
_pow(obj,obj) return object 1 to the power of object 2
_gcd(obj,obj) return Greatest Common Divisor of two objects
_zeros(obj) return number of trailing decimal zeros

Input strings come in as unsigned but with prefix (i.e. as '123', '0xabc' or '0b1101').

Testing of input parameter validity is done by the caller, so you need not worry about underflow (f.i. in _sub(), _dec()) nor about division by zero or similar cases.

The first parameter can be modified, that includes the possibility that you return a reference to a completely different object instead. Although keeping the reference and just changing it's contents is prefered over creating and returning a different reference.

Return values are always references to objects or strings. Exceptions are _lsft() and _rsft(), which return undef if they can not shift the argument. This is used to delegate shifting of bases different than the one you can support back to Math::BigInt, which will use some generic code to calculate the result.

If you want to port your own favourite c-lib for big numbers to the Math::BigInt interface, you can take any of the already existing modules as a rough guideline. You should really wrap up the latest BigInt and BigFloat testsuites with your module, and replace in them any of the following:

use Math::BigInt;

by this:

use Math::BigInt lib => 'yourlib';

This way you ensure that your library really works 100% within Math::BigInt.